Resummed Higgs cross section at N3LL

Abstract

We present accurate predictions for the inclusive production of a Higgs boson in proton-proton collisions, via gluon-gluon fusion. Our calculation includes nextto-next-to-leading order (NNLO) corrections in perturbative QCD, as well as the resummation of threshold-enhanced contributions to next-to-next-to-next-to-leading logarithmic (N 3 LL) accuracy, with the inclusion of the recently-determined three-loop constant coefficient (sometimes referred to as N 3 LL accuracy).Our result correctly accounts for finite top, bottom and charm masses at leading order (LO) and next-to-leading order (NLO), and includes top mass dependence at NNLO. At the resummed level the dependence on top, bottom and charm mass is accounted for at NLL, while only the top mass at NNLL. The all-order calculation is improved by a suitable choice of the soft terms, dictated by analyticity conditions and by the inclusion of subleading corrections of collinear origin, which improve the accuracy of the resummation away from the threshold region.We present results for different collider energies and we study perturbative uncertainties by varying renormalization and factorization scales. We find that, at current LHC energies, the resummation corrects the NNLO result by as much as 20% at µ R = µ F = m H , while the correction is much smaller, 5.5%, at µ R = µ F = m H / 2. While the central value of NNLO+N 3 LL result depends very mildly on the scale choice, we argue that a more realiable estimate of the theoretical uncertainty is found if the perturbative scales are canonically varied about m H .

On the Higgs cross section at N3LO+N3LL and its uncertainty

“…In the same way as fixed-order calculations can be performed at different (N k LO) accuracy, resummed calculations can be systematically improved by including next k -to-leading logarithmic (N k LL) corrections. Threshold resummation for Higgs production is currently known to N 3 LL [13][14][15][16]. In this work we update the results of refs.…”

“…In this work we update the results of refs. [13], in view of the recently computed N 3 LO result [9][10][11][12]. We discuss the impact of the resummation on the central value and we suggest a robust way of estimating the theoretical uncertainty due to missing higher orders, which goes beyond traditional scale variation.…”

Toward NNLL threshold resummation for hadron pair production in hadronic collisions

“…According to (6), the second delta-function implies that η = 1 2 ln(x a /x b ). At next-to-leading order (NLO), or overall O(α 3 s ), one can haveτ = 1 andη = 0.…”

“…The most advanced results have been obtained for color-singlet processes such as Higgs production, where NNLL [4,5] and, most recently, even studies up to the N 3 LL level [6,7] have been obtained, in which seven towers of logarithms are fully taken into account to all orders. This became possible when all threshold distributions at three-loop order were computed [8].…”

Resummed Differential Cross Sections for Top-Quark Pairs at the LHC

“…This procedure relies on an efficient construction of Mellin-transformed parton luminosities, for which we use methods outlined in Refs. [14,15].…”